AMNA NAWAZ: If the government were not shut down, we would have received the latest official report today on jobs and unemployment.

Instead, it's the second straight missing report, leaving employers, workers and policymakers trying to understand the labor picture without crucial data.

One thing seems clear.

The labor market may not be cratering, but it doesn't look very strong.

This week, one private report found 42,000 new jobs were created last month.

Then a separate report found that more than 150,000 jobs were cut in October, the highest in over two decades and tied in part to the A.I.

boom.

Paul Solman has been looking into the most recent official unemployment numbers and questions over whether the government's own measurements are outdated.

PAUL SOLMAN: Joe Biden.

JOE BIDEN, Former President of the United States: I know some wanted to see a larger number today, and so did I. PAUL SOLMAN: George W. Bush.

GEORGE W. BUSH, Former President of the United States: The fundamentals are strong.

We're just in a rough patch.

PAUL SOLMAN: Barack Obama.

BARACK OBAMA, Former President of the United States: It's a reminder that we're still in the middle of a very deep recession.

PAUL SOLMAN: Donald Trump is not the first recent president vexed by a dreary number of jobs created, but he is the first to declare war on the data.

DONALD TRUMP, President of the United States: We're doing so well.

I believe the numbers were phony.

So you know what I did?

I fired her.

QUESTION: Right.

(CROSSTALK) DONALD TRUMP: And you know what?

I did the right thing.

PAUL SOLMAN: Which her?

Erika McEntarfer, then commissioner of the Billions, the Bureau of Labor Statistics.

In August, hours after a BLS report showing slow job growth and large downward revisions for previous months, Trump canned her, claiming she'd rigged the totals to make him look bad.

DONALD TRUMP: These numbers just came out, by the way.

PAUL SOLMAN: Now, few outside the White House think the BLS ever cooks the books, but plenty of Americans might agree that something seems wrong with the other BLS number that comes out every month tracking the job market, the unemployment rate.

It's barely 4 percent, less than the average of every decade since the 1960s.

Yet two-thirds of us workers now report living paycheck to paycheck.

SHELBY GLOVER, Gig Worker: The job search has been rough.

PAUL SOLMAN: Like 33-year-old marketing pro Shelby Glover, laid off in 2023.

She now works three jobs to make ends meet.

SHELBY GLOVER: I don't remember a time, even when I was in my early 20s, where it has felt this difficult.

EUGENE LUDWIG, Former U.S.

Comptroller of the Currency: Producing numbers, headline numbers that are reported every month that produce a rosier picture than is in fact lived reality misleads the American people and misleads policymakers, and it has very serious implications.

PAUL SOLMAN: Former Comptroller of the Currency Eugene Ludwig says the problem is how the BLS defines unemployment.

EUGENE LUDWIG: When we think of as employed, right, we think of somebody having at least enough of a job that they can eat and have the roof over their head.

But when we put out these numbers and say, hey, only 4.3 percent of the American people are unemployed, we think of a world that is quite different than the reality that people are facing.

PAUL SOLMAN: The headline unemployment rate measures the percentage of Americans looking for work who can't find any.

Each month, the BLS calls some 60,000 household, and they ask about a recent week, says Erica Groshen, who ran the BLS from 2013 to 2017.

ERICA GROSHEN, Former Commissioner, Bureau of Labor Statistics: During that one week, did you work for at least one hour for pay or profit?

PAUL SOLMAN: There are other questions, but, yes, one hour in a week and the BLS says you're employed.

EUGENE LUDWIG: These definitions were established in the 1930s, and it was much more typical for somebody either to have a job, factory job or whatever, or not to have one.

Our gig economy, where we have a high percentage of the population with short-term gigs, is a different world.

And the statistical resources in the government haven't accommodated to that.

PAUL SOLMAN: So, claims Ludwig, the unemployment numbers ignore millions of Americans who either can't find as much work as they want or don't earn more than $25,000 a year, functionally unemployed, he calls them, people like Bryan Box, a forester in Athens, Georgia.

Do you consider yourself employed?

BRYAN BOX, Forester: I don't consider myself fully employed.

I can definitely work a heck of a lot more than I am now.

PAUL SOLMAN: Box hasn't actually cashed a paycheck in months while doing prep work for next season, but anyone who works for themselves one hour in the reference week, even if for zero or negative income, is employed.

And are you making enough to live?

BRYAN BOX: Right now, the only way my finances make sense are because of my family helping me out.

It's really, really tough.

I hate being - - I hate feeling like I'm a burden to others.

PAUL SOLMAN: Shelby Glover is struggling too.

SHELBY GLOVER: I have put in dozens and dozens of resumes, and maybe once or twice made it to an actual interview.

PAUL SOLMAN: When you see the headline numbers of low unemployment, for example, just barely over 4 percent, what's your reaction?

SHELBY GLOVER: It is a little hard to believe.

I mean, right now, at this point, I am employed, but I'm not fully employed.

PAUL SOLMAN: In fact, more than a quarter of the labor force now does gig jobs, says the workers lab at Johns Hopkins, driving for Uber, pet sitting, et cetera.

And for about one in 10 of us, gig work is the primary source of income.

Thus, concludes Ludwig: EUGENE LUDWIG: The more that we have hard time work, where people really want to have a full-time job, and the more that we don't pay people a living wage, our calculation would show that, in fact, as a practical matter, in terms of a functional matter, they're really unemployed.

PAUL SOLMAN: So what do you calculate the real functional unemployment rate to be?

EUGENE LUDWIG: The functional unemployment rate is between 24 and 25 percent today, moving closer to 25 percent.

PAUL SOLMAN: Former BLS head Erica Groshen doesn't dispute the math, but she thinks the agency's headline number is the standard for a reason.

ERICA GROSHEN: One number is never going to tell you everything you want to know if you care about the labor market.

But there is value in having a headline number that everybody understands.

PAUL SOLMAN: Now, the BLS does report a broader unemployment number, known as U, for unemployment, 6, which includes many, though not all of us, who've stopped looking for work.

They almost double the headline rate to 8.1 percent.

Add in everyone who says they want a job, around 11.5 percent.

But you never even hear about U-6.

Seems like an increasingly jarring disjunction between the headline number and the reality for most Americans.

ERICA GROSHEN: It's not up to the BLS to make that case itself, right?

BLS is not a political or advocacy organization.

PAUL SOLMAN: In the meantime, says Ludwig: EUGENE LUDWIG: Twenty-five percent of the American people right now are functionally unemployed.

If you don't say that, 4.3 percent makes you feel, hey, we're -- you're doing pretty well.

It paints a much rosier picture, and it causes policymakers not to take the problem as seriously as it really is.

PAUL SOLMAN: One presidential candidate who did tap into that idea back in 2016 was Donald Trump, who spoke about it after a primary win in New Hampshire.

DONALD TRUMP: Don't believe those phony numbers when you hear 4.9 and 5 percent unemployment.

The number is probably 28, 29, as high as 35.

If we had 5 percent unemployment, you really think we'd have these gatherings?

PAUL SOLMAN: Nearly nine years later, President Trump has, well, changed his mind.

For the "PBS News Hour," Paul Solman.